In theoretical physics, an M2-brane, is a spatially extended mathematical object that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume.
The M2-brane solution can be found by requiring ( P o i n c a r e ) 3 × S O ( 8 ) symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three-form gauge field which, in isotropic coordinates, can be written as
d s M 2 2 = ( 1 + q r 6 ) − 2 3 d x μ d x ν η μ ν + ( 1 + q r 6 ) 1 3 d x i d x j δ i j F i μ 1 μ 2 μ 3 = ϵ μ 1 μ 2 μ 3 ∂ i ( 1 + q r 6 ) − 1 , μ = 1 , … , 3 i = 4 , … , 11 , where η is the flat-space metric and the distinction has been made between world volume x μ and transverse x i coordinates. The constant q is proportional to the charge of the brane which is given by the integral of F over the boundary of the transverse space of the brane.
